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arXiv · 2411.01413

Kupershmidt operators on $3$-BiHom-Poisson color algebras and $3$-BiHom-pre-Poisson color algebras structures

Othmen Ncib·Sergei Silvestrov
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Abstract

The purpose of this paper is to introduce the class of noncommutative $3$-BiHom-Poisson color algebras, which is a combination of $3$-BiHom-Lie color algebras and BiHom-associative color algebras under a compatibility condition, called BiHom-Leibniz color identity, and then study their representations and associated Kupershmidt operators. In addition, we introduce the notion of noncommutative $3$-BiHom-pre-Poisson color algebras and investigate the relationship between noncommutative $3$-BiHom-Poisson color algebras and $3$-BiHom-pre-Poisson color algebras via Kupershmidt operators.

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Othmen Ncib, Sergei Silvestrov. 2024-11-03. Kupershmidt operators on $3$-BiHom-Poisson color algebras and $3$-BiHom-pre-Poisson color algebras structures. https://arxiv.org/abs/2411.01413

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